砂性土渗流的分形特征研究

Research on fractal characteristics of permeability of sandy soil

针对砂性土颗粒结构的复杂性和不规则性,从颗粒级配和达西定律出发,基于分形几何理论,通过颗粒分析和渗透试验,建立了砂性土颗粒级配分形维数与不均匀系数的关系,从而揭示了级配分形维数的物理意义;通过线性回归,进一步探讨了级配分形维数与渗透系数之间的相关关系。研究发现:级配越好,不均匀系数越大,分维越小,渗透系数也越小。结果表明,级配分形维数是刻画砂性土的颗粒组成及其级配特征的有效参数,直观定量地描述了土的渗透性能,从而为多孔介质以及断层破碎带等裂隙介质的渗透性研究提供了一种较好的研究思路。

Based on the fractal geometry theory, according to the granulometry and infiltration test, the relation between the fractal dimension of grain composition and coefficient of non-uniformity was established from the grain composition and Darcy law. The physical meaning of the fractal dimension of grain composition was demonstrated by considering the complexity and irregularity of the granular structure of sandy soil. Furthermore, the relation between the fractal dimension of grain composition and permeability coefficient was discussed by using linear regression analysis. The study shows that the better the grain composition is, the greater the coefficient of non-uniformity, the smaller both the fractal dimension and the permeability coefficient. The result indicates that the fractal dimension of the grain composition, which describes the permeability of sandy soil quantitatively and directly, is an effective parameter for describing the size composition of sandy soil and its grain composition characteristics. As a result, this paper provides a new way for research on the permeability of the porous medium as well as the fractured porous medium.